Blades for axial flow compressors and turbines



' Aug- 26, 19 7- A. R. HOWELL 3 4 amass ron mu. no! ,cournassons Mb 'runsnuss I Filed Jim. 10, 1944 2 snap-sum 1 FIG. 2.

Aug. 26, 1947. A. R. HOWELL 2,426,270

BLADES AXIAL FLO COIXRESSORS AND TURBINES Filed June 10, 1944 2 sheets-sheet 2 Y Patente stares PATENT OFFICE j fzszazvo a Alnn Raymond Howell, Neath, England, as'signor to Power Jets (Research and Development) Ltd, London, England, a British company Application June 10, 1944, Serial No. 539,731

In Great Britain April 5, 1943 Section 1, Public Law 690, August a, 1946.

- Patent expires April 5, 196:; a f

This invention relates to compressors, turbines, and like rotary powerconversion' machines, operating with compressible viscous fluids, and more particularly to the bladingof axial flow stages of such machines. I

An object ofthe invention is to provide blades appropriately shaped in regard to their leading angle, trailing angle, chord angle and aerofoil profile to conform to a possible and stable fluid flow pattern. Other objects of the invention are to provide blading conforming to or/and imposing on the fluid a flow patternhaving one or more advantageous characteristics as hereinafter set forth or/ and to provide blading whose geometical properties facilitate manufacture.

In the design of blades for such machines various empiricaland arbitrary laws have been a proposed to which the designs of blades are toconform, but with the exception of one type of blading, hereinafter referred to as free vortex" blading, the blade shapes so developed may and frequentlydo postulate fluid'flow patterns which mps.

r 16 Claims. (01. 230-123) distribution of their leading and trailing angles) as to conform to a radial distribution of entry and discharge velocities of the working fluid, such that the diflerence of the whirl velocities, at entry and discharge respectively of the blade row in question, is in inverse proportionality to the radial distance from the rotational axis of the machine,.but excluding blades of the free-vortex form as hereinbefore defined. Y

The invention also includes compressors, pumps, turbines and like rotary power conversion machines operatingwith compressible viscous fluids and comprising a single row of rotor blades or rows of rotor blades rotating at the same or 7 are either impossible because they do not satisfy necessary conditions of continuity or equilibrium, or, alternatively are unstable.

It has been pointed out in Whittle U. 8 Patent 2,378,372 that the characteristics of the flow from a stator nozzle ring of a turbine, or the discharge from the rotor of an axial flow compressor, tend to approximate to the characteristics of afree vortex and the said specification describes and claims blades which are shaped to conform to such a vortex flow pattern at entry. and discharge; and such blades are known as "free-vortex" blades and will hereinafter be so referred to.

I have found, however, that it is possible to design blades which satisfy the condition of conforming to a stable flow pattern whichcan actually exist in thema'chine, to a sufflcient degree of approximation for practical purposes,

otherwise than by designing to the "free-vortex shape as set out in the above-mentioned patent specification No. 2,378,372 provided that the blade shape satisfies certain other requirements to be hereinafter set forth; and .that these requirements give sufficient latitude to the designer tosatisfy at least some of a number of other possible requirements concerned more especially with the aerodynamic characteristics of the blades or of the machine in which they are incorporated and such matters as ease of manufacture.

According to the present invention, a row of blades in a rotary power'conversion machine of the type herein first referred to, comprises individual blades so shaped, (in respect of the radial different speeds in the same or different directions with or without one or more rows of stator or stationary blades; whereinthe blades of at least one row of blading, constituting or forming part of, an axial fiow stage, are shaped as set forth in the preceding paragraph.

It will be seen that this does not imply that the actual whirl velocity at entry or at discharge necessarily follows the law of inverse proportionality to the radial distance as is the case with free vortex blading, but it is only the increment (positive or negative) of whirl velocity acquired 'by the fluid in passing through the blading row.

stitute a limiting case of blading in accordance with this invention.

In amplification of the foregoing statement, the leading and trailing angles of the blade are defined by the tangents to the centre line of the blade profile at the leading and trailing edges, and the blade is said to conform to the (assigned) entry and discharge velocities, if the entry is without shock and the trailing angle of the blade is substantially the same as the discharge angle of the fluid.

Entry without shock is obtained if the leading angle. of' the blade is within 10 of the" fluid entry angle (averaged over the-circumference of the blade row), though for turbine blades, especially reaction blades, substantially shockless entry is obtained with somewhat greater departures of the blade leading angle from the fluid entry angle.

Further, any assigned distribution of fluid velocities must satisfy the well known velocity triangle relations and the axial components of these velocities must satisfy the condition of continuity'of flow.

To recapitulate, blading in accordance-with this 3 invention and constituting a row of rotor or stator blading will be so shaped as substantially to satisfy the following condition, viz;

The blades conform (as herein defined) to some possible assigned distribution of fluid velocities at entry and discharge (of the blade row considered) in which the difierence between the whirl velocities at entry and discharge respectively is in inverse proportionality to the radial distance from the axis of rotation; but the absolute whirl velocities at entry to and discharge from the blades are not in inverse proportionality to the radial'dlstance as with free vortex blades.

As will hereinafter be shown, the satisfaction of this condition does not uniquely determine the shape of the blade, but allows some latitudein the design. When one blade row only is under consideration, the radial distribution of any one of the following parameters, viz: entry angle, discharge angle, and chord angle (namely the angle between the axial direction and a line joining the leading and trailing edges of the blade at the same radial distance from the axis of rotation), may be selected to fulfil some particular design requirement; or, when two consecutive blade rows are considered, the radial distributions of any two of the three pairs of the abovementioned parameters may be so selected. The particular design requirements, as yet unspecified, to be satisfied by the above-mentioned selection will be more fully discussed hereinafter.

Figure 1 is a diagram of the blades of an axial flow machine according to this invention.

Figure 2 is a velocity diagram corresponding to the blading of Figure 1.

Figure 3 is a diagram illustrating radial distribution of velocities over a blade according to this invention.

The invention is explained graphically with the aid of the accompanying diagrams relating to a stage which is taken to consist of two adjacent blade rows, whether rotor or stator or both rotors. Figure 1 diagrammatically illustrates the two blade rows I and 2 at any radius r, the actual blading shown being of the type used for axial compressors. 3 and 4 are the leading edges of the blades in rows l and 2 respectively while 5 and 6 'are the respective trailing edges of the blades. The axial direction of flow is indicated by the arrow 1. The dotted blade row 8 is the previous blade row, if existing, to the first row considered. The peripheral velocity of the first blade row, second blade row and previous blade row are denoted by U1, U2 and U0 respectively and are positive if taken in the direction of the arrows shown in Fig. 1. If any blade row is stationary then the corresponding U value is zero. The angles A, B, C, D and E in Fig. 1 denote the direc tion of the fluid relative to the blades at outlet from the previous row, inlet to first row, outlet from first row,, inlet to second row, and outlet from second ro respectively; all the angles being measured from. the axial direction. The chord angle will be measured from the axial direction, the angle being positive for the arrangement shown in Fig. 1. i

The velocity triangles corresponding to the blade rows of Fig. 1 at any radius r are shown in Fig. 2, where W1, Wrand We are respectively .the axial components of the velocities before the first row I, before the second row 2 and after the second row 2, VA, V3, V0, Va, and Vi: are the fluid velocities relative to the blades at inlet and outlet corresponding to the fluid angles A, B, C,

'D and E respectively. The peripheral velocities U0, U1, U;, are represented by the lengths PQ, HQ, and RS, respectively and the absolute fluid velocities are represented by chain-dotted lines. From these velocity triangles it can easily be proved by geometry that U0+Ul=W1 (tan A-i-tan B) U1+U2=W2 (tan C+tan D) also V2, VB, Vc, VD and Va are respectively equal to W1 see. A, W1 sec. B, W2 sec. C, W2 sec. D and U, U,- W, tan 0- (1, 11". tan

Similarly for the second row the work done per unit mass is equal to U2X (W2 tan D-Wa tan E) (4) In considering an actual design, it is usual to fix on a design radius Td and to assume that the values of the peripheral velocities U0, U1 and U2, the axial velocity components W1, W2 and Wz,'the work required to be done in each blade row and the outlet angle A from the previous blade row, are known. The four unknowns left at this radius would then be the angles B, C, D and E and these angles can be determined by making use of the two velocity triangle Equations 1 and 2 and the two work done Equations 3 and 4 of the previous paragraph. From tests of blades in cascade, which are well known to'blade designers, it is possible to pick on the blade profiles which when appropriately spaced and placed at the correct chord angle will satisfy the above fluid outlet angles C and E and the condition of entry without shock as previously defined.

Having determined the blading at the design radius Td, it remains to evaluate the corresponding radial distributions of angles and velocities. At any other radius r, in a similar manner to that at the design radius, there will be the two velocity triangle equations coupled with two other equations, one for each row satisfying the condition constituting the basis of this invention, viz:

(W1 tan B-W2, tan C)r=const. (3a) (W2 tan DW3 tan E) 1'=const. (4a) There are thus four equations in all containing eight unknowns), viz. the five angles A, B, C, D

.and E and the radial distributions of the axial velocities as defined by the ratios of W1, W2 and W: to their respective values at the design radius. The eight unknowns are reductible to six by stipulating that the radial distributions of all three axial velocity components W1, W2, W: are the same, i. e. that at any given radius 11 32 =Ha 'WIO W20 W30 this invention will be many and asphalt de-, fined by selecting the radial distributions of any two of the following variables, viz: the absolute one blade row or one may be associated with. one

blade row, and the other with the other blade row.

Though the method of design given will apply to any detirable radial distribution of the axial components of the fluid velocities, it is-normally convenient bolic radial distribution, the latter distribution being appropriate for taking into account boundary layer and secondary effects. When using-a parabolic distribution the velocities'chosen at the blade ends in the boundary layer are preferably not zero as such a distribution requires poor blade profiles at points located in the boundary layers. It is better to design to a radial distribution which flts -more closely to theideal conditions over the v greater part of the blade height and then finishes 'with finite velocities at the blade ends.

An example of such a parabolic distribution is shown in Fig. 3 where the axial component of velocity W is plotted in the direction 9 between the bounding walls 10 and II of the annular passage through which the fluid flows in acompressor'or turbine. The selected W distribution is indicated by the curve I! and its mean value by the line and arrow l3. Arrows l4 and IS indicate the maximum and minimum values of W respectively. For parabolic. distributions it can easily be proved that W minimum=3W(meai1) '2W(maximum) The valuesof W(mean)/W(maximum) which appear desirable to use are normally between 0.85 and 0.95 for compressors and between 0.9 and 1.0 for turbines.

For flows which are incompressible or only slightly compressible the fluid velocity gives a good criterion for' detrimental effects with especial reference to cavitation. When however velocities become large and the flow is highly compressible, the local Mach number is a better criterion having regard especially to detrimental compressibility effects. The Mach number is defined as the velocity relative t o the blade at the point considered divided by the local acoustic velocity. The local acoustic velocity will generally vary radially but its radial variation can be neglected for the slightly compressible flows. Radial distributions to consider either a constant or paraof velocity and Mach number will be hereinafter tions), while complying with the necessary revquirements of continuity of flow and velocity triangle relationships and'also with the basic requirementpi this invention formulated in Equations 3a and 4a, offers to the designera very wide choice of possible blade forms.

In what follows, certain desirable design characteristics and their influence on this selection will be further discussed, but before doing so it will be convenient to. describe in detail, by way of example, one typical embodiment of the invention asapplied to a single, axial flow, compressor stage, consisting of a row of rotor blades followed and preceded by rows of stator blades, all as illustrated'in Figs. 1 and 2. It will therefore be seen that The following design data are postulated:

Insideradius (for each row) 'inches '6 Outside radius (for each row) ..do 8 R. P. 10,000 Rate of doing work on the fluid H. P. per lb. of fluid 9.3 Mean axial fluid velocity for each row.

ft/sec-.. 450

Whirl velocities at outlet of both stator rows, at the inside radius, are zero. so that, at this radius,

tan A=tan E=0- The selected radial distributions are:

(15 Axial fluidvelocity is constant along the radius: hence,

W1'=W2=Wa=450 ft./sec. at all radii (2) To reduce compressibility effects on the second stator blade row, the inlet fluid velocity of that row is constant along the radius, i. e.

tan D=const.-

i if gg a" 1" a" Obtained from- U1. ft./sec.. 525 612. 5 700 W1: Wa= W3. 450 450 450 Arbitrary Selection. tan A+tan B l. 167 l. 361 1.555 Velocity triangle relations. tun C+tan D l. 167 1.361 1.555 Velocity triangle rela- 1 ions. tan Btan 0.... 0.700 0.600 0. 525 Equations 34:, 4a. tan D--tan E... 0700- 0.600 0. 525 Equations 3a, 4a.

1. 261 l. 380 0. 601 0. 855 0. 700 0. 700 Arbitrary Selection. 0.100 0.175 A From tests of blades in cascade, which are well known to blade designers it is possible to pick on the blade profiles which when appropriately spaced and placed at the correct chord angle will give thedesired'fluid outlet angles for the above example and will engage the fluid at inlet without shock.

The blades are spaced sufllciently close to' avoid the lift coeiflcient becoming so great as to stall the blades. A convenient definition of lift coefficient is given by the theoretical coeflicient Cr. corresponding to the fluid deflection but neglecting losses. This coefllcient is given "by Where L andM are the inlet and outlet fluid angles respectively, Sis the circumferential spacing and C the blade chord, the latter being the distance between the leading and trailing edges of the blade. The angle N is given by tau N=% (tau L+tau M) The desirable values of C1. for design vary considerably with the type of profile used and the condition of operation, such as Mach number; so it is preferable to use cascade test data for determining the spacing. However, present day design values for C1. at the mean radius appear to be given approximately by the following formula.

Where V1. and Vm are the inlet and outlet fluid velocities respectively and a: varies between 1.7

' and 2.3. For compressor blades, that is when V1. is greater than Vn, y varies between 2.5 and 3.0. For turbine blades when VL is less than Vm the value of y appears to be about zero, or in other words C1.=:r and therefore varies between 1.7 and 2.3. For the above example, relating to a compressor, as hereinbefore described, an appropriate spacing/chord for the rotating blade at mean radius would be about 1.0, the values of CL and (VL/Vn) being approximately 0.9 and 1.35 respectively.

The explanation and example previously given have been taken for a compressor stage of two rows of blades. The difierence for a turbine'stage is simply that the outlet fluid angles A, C and E will normally be of negative sign giving again normally negative values for the peripheral velocities U0, U1 and U2 and for the work done at the design radius, as with turbines energy is taken from the fluid, while with compressors energy is imparted to the fluid.

In the typical example above described the variables whose radial distributions were selected to complete thedefinitions of the blade forms were the axial velocity profile and the inlet fluid velocity of the second stator blade row, the latter being selected for its influence on compressibility effects. Other possibilities will now be briefly discussed.

Of the various favourable design characteristics which may be aimed at, some of the more important are as follows: a

(a) Control of axial velocity distributions: this has already been discussed.

(b) Ease of blade manufacture: simplification of blade shape for this purpose may dictate the radial distribution of one or both the variables at the designers disposal.

(c Suppression of detrimental compressibility effects or/and cavitation; this calls for a favourable radial distribution of either the fluid inlet angle or fluid inlet velocity in the case of compressors, or in the case of turbines the fluid outlet angle or outlet velocity. As already mentioned, for high velocities or/and highly compressi'ble flows the Mach number distribution is more important than the actual velocity distribution and is therefore preferably selected.

Specific types of blading, in accordance with the invention, which are designed to meet one or more of the above requirements fall naturally into two main groups:

(A) Those for which (a) control of axial velocity distribution is an over-riding consideration.

(B) Those in which close control of axial velocity distribution is not attempted, but more complete satisfaction of requirements (b) or/and (c) is sought.

Both. these groups can be sub-divided into two sub-groups according to whether the blading is intended for a compressor or a turbine.

Within these groups I distinguish thirteen varieties of blade design of especial utility, though it must be understood that this list is not considered to be exhaustive.

In 'group A, one of the variables selectively determined is the axial velocity whose radial distribution may be either constant (as in the specific example hereinbefore described in detail) or parabolic as hereinbefore mentioned; this leaves one other variable only at the designers choice, which may be exercised as follows:

(1) One blade row (rotor or stator) of the stage has untwisted blades of constant blade section.

(2) One blade row (rotor or stator) of the stage has blades of constant chord angle but varying blade section,

Varieties (l) and (2) are designed to meet requirement (b) above, ease of manufacture; variety (2) has a better aerodynamic performance than (1).

(3,) One blade row (rotor or stator) of the stage has constant fluid inlet angle, inlet velocity or inlet Mach number.

In (4) the fluid inlet angles, inlet velocities or inlet Mach numbers of both blade rows of the stage at the same radius are equal or in constant proportionality, but the actual radial distributions of any of these variables are not arbitrarily selected.

In (5) the radial distribution of fluid inlet angle, inlet velocity or inlet Mach number of one blade row (rotor or stator) of the stage is so selected as to minimise compressibility or cavitation efiects at every radial station, e. g. so that the variation of the Mach number is in the sense opposed to the variation of thickness of section, i. e. the highest Mach number is associated with the thinnest section and conversely.

Varieties (3), (4) and (5) belong to the compressor sub-group and varieties (6), ('7) and (8) belonging to the turbine sug-group are similar to (3), (4) and (5) respectively but with the word "outlet substituted throughout for inlet.

In group (B) are varieties (9) to (13), defined as follows: (9) is similar to (2) but the limitation of constant chord angle is applied to the blades of both rows. (10), (11), (12) and (13) correspond respectively to (3), (5), (6) and (8) but the stated limitations on fluid angles, velocities and Mach numbers are applied to both rows of blades; in varieties (l0) and (12), the constant values imposed on the fluid inlet or outlet angle, inlet or outlet velocity or inlet or outlet Mach number are not necessarily the same for both blade rows.

Varieties (l0) and (11) belong to the compressor" sub-group and (12) and (13) to the "turbine sub-groups. Varieties (l), (2) and (9) are applicable either to turbines or compressors. L

The foregoing sets out the manner in which typical blade formations are obtained, but it will be understood that these may with advantage be slightly modified in practice for manufacturing or stress reasons, e. g. to give linear twists, linear tapers in chord or/and thickness, straight leading or/and trailing edges or straight line development between two arbitrarily selected radial stations of the blade, to enable the blades is; be withdrawn from dies without splitting the to conform to a fluid flow across said row of blades, in which flow the local magnitudes at each radial distance from the axis of rotation of said blade row of the peripheral components of the absolute fluid velocities before entering and f after-leaving said blade row respectively diifer by an amount substantially inversely proportional to said radial distance, being, themselves related to said radial distance otherwise than in inverse proportionality.

2. A rotary turbine type power conversionmachine for use with a, compressible viscous working fluid, including at least two consecutive and coaxial rowsof axial flow type blades having leading and trailing edges, whereof one row at least is a row of rotative blades, all of said blades 1 being so shaped and so operatively positioned that the angles of the blades at saidedges are .varied along the blades to conform to a fluid flow across each of said rows of blades, in'which flow the local magnitudes, at each radial distance from the common axis of the blade rows, of the peripheral components of the absolute fluid velocities before entering and after leaving the concerned blade row respectively, differ by an amount substantially inversely proportional to said radial distance, being themselves related to said radial distance otherwise than in inverse proportionality. I

3. A rotary turbine type power conversion machinefo;- use with a compressible viscous working fluid, including at least'one rotative row of axial flow type blades having leading and trailing edges, the shapes and operative ositionsof said blades being characterised by entry and discharge blade angles 13 and C, at said leading and trailing edges respectively, which angles vary along the blades substantially in conformity. with the relations (W tan B- W: tan C)fr=constant 12W; tan B constant 1'.W tan C constant in which" relations is the radial distance from the axis of rotation of the blade row, the angles B and C being measured from a plane perpendicular to saidaxis, and W1, We are the velocal magnitudes, corresponding to each value machine for usewith a compressible viscous work-- ing the blade row being likewise substantiallyconstant at all radial distances from said axis.

ing fluid, including at least two consecutive and I coaxial rows of axial flow type blades having leading and'trailing edges, whereof at least one row is a row of rotative blades, the shapes and operative positions of the blades of the first of said blade rows being characterised by entry and discharge blade angles EB and C, at said leading and trailing edges respectively, the blades of the relations 12W, tan B constant r. W, tan C constant r.W, tan D constant 03W; tan E constant in which relations. 1' is the radial distance fromthe common axis of the blade rows, the

, angles B, C, D, E are measured from a plane perpendicular to said axis, and W1, W2 W3 are the local magnitudes, corresponding to each value of the radial distance r, of the axial components .of fluid-velocity, before entering the first ,blade row, intermediate to twoblade rows and after leaving the second blade rowrespectively.

' 5. A rotary turbine type power conversion machine as claimed in claim 1, wherein the blades of the mentioned rotative blade row are further so shaped and operatively positioned that the angles of theblades at their leading and trailing I edges are varied along the blades to conform to a fluid flow across the said row of blades, wherein the axial component of the velocity of the fluid before entering the blade row is substantially constant at all radial distances from the axis of rotation, the axial velocity component after leavafter leaving the blade row being likewise substantially constant at all said axis.

7. A rotary turbine type power conversion machine as claimed in claim 1, wherein the blades of the mentioned rotative blade row are further so shaped and operatively positioned that the angles of the blades at their leading and trailing edges are varied along the blades to conform to a fluid flow across thesaid row of blades, wherein the axial component of the velocity of the fluid before entering the, blade row varies with the radial distance from the axis of rotation in such a way that its value is least at the ends of the blade and greatestmidway between said ends and at intermediate points is such that, when plotted against said radial distance its values lie substantially on a parabola having its vertex midway between the blade ends, and wherein the axial velocity component or the fluid flow after leaving the blade row varies with respect to the radial distance from the axis of rotation in asimilar manner.

8. A rotary turbine type power conversion machine as claimed in claim '2, wherein the radial distances from blades of at least one of the mentioned blade the velocity of the fluid before'entering the blade row varies with the radial distance from the axis of rotation in, such a way that its value is least at the ends of the blade and greatest midway between said ends and at intermediate. points is one parameter selected from the angle, ,the vesuch that, when plotted against said radial distance its values lie substantially on a parabola having its vertex between the blade ends, and wherein the axial velocity component of the fluid flow after leaving the blade row varies with respect to the radial distance from the axis of rotation in a similar manner.

9. A rotary turbine type power conversion machine as claimed in claim 2, wherein the blades of at least one of the mentioned. blade rows are further so shaped and operatively positioned that the variation along the :blades of the blade angle at their leading edges conforms to a fluid flow across the blade row, oflwhich fiow locity and the Mach number of the flow of fluid relative to the blades before entering the blade row is substantially constant at all radial disstances from the mentioned common axis.

10. A rotary turbine type power conversion machine as claimed in claim 2, wherein the blades of at least one of the mentioned blade rows are further so shaped and operatively positioned that the variation along'the blades of the blade angle at their trailing edges conforms to a fluid flow across the blade row, of which fiow one parameter selected from the angle, the velocity and the Mach number of the flow 'of fluid relative to the blades after leaving the blade row is substantially constant at all radial distances from the mentioned common axis.

11. A rotary turbine type power conversion machine as claimed in claim 2, wherein the blades of at least one of the mentioned blade rows are further so shaped and operatively positioned that the variation along the blades of the blade angle at their leading edges conforms to a fluid flow across the blade row, of which flow one parameter selected from the angle, the velocity and the Mach number of the flow of fluid relative to the blades before entering the blade row is appropriately related to the blade thickness at every radial distance from the mentioned common axis for minimising the effects associated with one of the following phenomena. 4

namely compressibility and cavitation, at all such radial distances, substantially as herein described.

12. A rotary turbine type power conversion machine as claimed in claim 2, wherein the blades of at least one of the mentioned blade rows are further so shaped and operatively positioned that the variation along the blades of the blade angle at their trailing edges conforms to a fluid flow across the ,blade row, of which 5.

12 such radial distances, substantially as herein described.

13. A rotary turbine type power conversion machine as claimed in claim 2, wherein the blades of both the mentioned blade rows are further so shaped and operatively positioned that the variation along the blades of the blade angle at their leading edges conforms to a fluid fiow across the blade rows, of which flow one parameter selected from the angle, the velocity and the Mach number of the flow of fluid before entering the first blade row and relative to the blades thereof is so related to a single corresponding and correspondingly selected parameter correspondingly associated with the second blade row that at all radial distances from the mentioned common axis the ratio of the first mentioned to the second mentioned of said parameters has a constant value, which may optionally be unity.

14. A rotary turbine type power conversion machine as claimed in claim 2, wherein the blades of both the mentioned blade rows are further so shaped and operatively positioned that the variation along the blades of the blade angle at their trailing edges conforms to a fluid flow across the blade rows, of which flow one parameter selected from the angle, the velocity and the Mach number of the flow of fluid after leaving the first blade row and relative to the blades thereof is so related to a single corresponding and correspondingly selected parameter correspondingly associated with the second blade row that at all radial distances from the mentioned common axis the ratio of the first mentioned to the second mentioned of said parameters has a constant value, which may optionally be unity. 15. A rotary turbine type power conversion machine as claimed in claim 2, wherein at least one of the mentioned blade rows has untwisted blades whose cross sectional profile is constant along the blade. g

16. A rotary turbine type power conversion machine as claimed in claim 2, wherein at least one of the mentioned blade rows has blades whose chord angle, being the angle between a line joining the leading and trailing edges of the blade at the same radial distance from the mentioned common axis and a plane perpendicular to said axis, is constant along the blade and whose cross sectional profile varies along the blade.

ALU'N RAYMOND HOWELL.

REFERENCES CITED The following references are of record in the file of this patent:

UNITED STATES PATENTS Number Name Date 1,926,446 Klosson Sept. 12, 1933 2,224,519 McIntyre Dec. 1!), 1940 5 Certificate of co ection li PatentN'o. 2,426,270. o

YALUN RAYMOND HOWELL v It is hereby certified that errore appear in the rinted specification numbered patent requiring correction as follows. olumn fi', line 311, for tau--- both occurrences, read tan; Column 7, line 3, for f tau three occurrences, read {an column 8,

line 45, for sug-group read sub-groumfland thatthe said'Letters Patent should be read with these corrections therein that the samemay conform to therecord of the casein the Patent Oflice. .c l -1 A Signed and sealed this 11th. daLy of November, A. D. 1947 THOMAS FLMUBPHYQ'Z;

- 'Augl ist 26, i947;

0fthe above Auiatant Gdnzmiesionefoflatenib, f 

